SIGMA AQL (Sigma Aquilae). Not one star, but two, not that you
could tell by a quick glance through the telescope, as the
components of this fifth magnitude (5.17) binary star in central Aquila (the Eagle) are so close as to be
visually inseparable. We know that Sigma Aql is double because two stars appear in the spectrum
(each showing their Doppler
shifts) and because every 1.95026 days they eclipse each other, the main
eclipse yielding a dip of about 0.2 magnitudes. If you like blue
stars, this one is for you, as the double consists of nearly
identical hot class B (B3) hydrogen-fusing dwarfs with estimated
temperatures of 18,500 Kelvin (though one source gives them as B3
and B4). From the ratio of the depth of the two eclipses (each
getting partially in front of the other every orbital revolution),
one is about ten percent brighter than the other. In the Milky Way, at 680 light years, the stellar
double is far enough to suffer 0.77 magnitudes of dimming by
interstellar dust. Were it absent, the star would shine at fourth
magnitude (4.40). That correction, the distance, and allowance for
ultraviolet light gives a combined luminosity of 2940 times that of
the Sun, and individual values of 1540 and
1400 Suns for Sigma Aql A and B, which in turn lead to radii of 3.8
and 3.7 times that of the Sun and (from the theory of stellar
structure and evolution) individual masses of 6 solar.
Kepler's third law then gives us an average separation of 0.07
Astronomical Units, or just 15 solar radii, not that much larger
than the sizes of the stars themselves. Analysis of the eclipses
and orbital velocities show a circular orbit that is tilted to the
plane of the sky by 72 degrees (to the line of sight by 18 degrees)
and again a separation of 0.07 AU. As a result of the tilt, the
eclipses are not total, but partial. Equatorial rotation speeds of
79 and 101 kilometers per second (corrected for the tilt, assuming
that the rotation and orbital axes are aligned) give rotation
periods of 2.3 and 1.9 days, close enough (given the inevitable
errors of measurement) to imply that the rotations are synchronized
with the orbital period, the stars always presenting the same
"face" to each other as a result of mutual tides. The tides and
the rapid rotation make the stars so oblate that, as they orbit,
they present different apparent disk sizes to us, enough so that
their combined brightness varies continuously even outside of
eclipse and makes the derivation of masses (a consistent 6.9 and
5.5 solar) much more difficult. As close as they are, however,
they are not sufficiently close that they transfer mass (that is,
they do not fill their zero-gravity tidal surfaces). That nice
state will end with evolution. The stars are about halfway through
their 30-million-year hydrogen-fusing lifetime. When the more
massive of the two gives up core hydrogen fusion and begins to
expand as a red giant, it will
encroach on its companion. If the dominant member were single, it
would eventually grow to a radius of 200 times solar, far larger
than the orbital size. As a result, one star will pass mass to the
other, and may even absorb the other in a merger in which much mass
will be lost to the system as well, the final result not really
very predictable. Nearly a minute of arc out from the system is a
12th magnitude "companion." It won't be watching the action,
however, because the apparent companionship is merely a line-of-
sight coincidence.